Rietveld Refinement

Practical Powder Diffraction Pattern Analysis using TOPAS

Robert E. Dinnebier, Andreas Leineweber, John S.O. Evans

• Publisher: De Gruyter
• Year: 2018
• Print ISBN: 9783110456219
• eBook ISBN: 9783110461404
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Geology & Earth Sciences

Almost 50 years have passed since the famous papers of Hugo Rietveld from the late sixties where he describes a method for the refinement of crystal structures from neutron powder diffraction data. Soon after, the potential of the method for laboratory X-ray powder diffraction was discovered. Although the method is now widely accepted, there are still many pitfalls in the theoretical understanding and in practical daily use.

This book closes the gap with a theoretical introduction for each chapter followed by a practical approach. The flexible macro type language of the Topas Rietveld software can be considered as the defacto standard.

1The powder diffraction method

Powder diffraction is one of the most powerful techniques for studying the atomic structure of real materials. In this chapter we assume the reader has a knowledge of basic crystallography and refer them to one of the excellent texts on the topic for more advanced information (e.g., Giacovazzo et al., 2011; Egami & Billinge, 2012). We will restrict ourselves to giving sufficient information that we can discuss diffraction phenomena that are particularly important for powder diffraction. We describe the basic effects of diffraction by crystalline and noncrystalline samples. We also discuss the origins of peak broadening in powder diffraction patterns and quantify how peak overlap leads to information loss relative to single crystal experiments. We refer readers to specialist texts (e.g., Pecharsky & Zavalij, 2009; Dinnebier & Billinge, 2008) for detailed information on experimental aspects of powder diffraction.

1.1Diffraction by crystallites

When radiation with a wavelength comparable to interatomic distances is incident on a crystallite, two types of coherent elastic scatterin...

Table of contents

• Cover
• Title Page
• Copyright
• Preface
• Contents
• 1 The powder diffraction method
• 2 The Rietveld method
• 3 Structure independent fitting
• 4 Peak shapes: Instrument ∘ microstructure
• 5 Quantitative phase analysis
• 6 Restraints, constraints and rigid bodies
• 7 Solving crystal structures using the Rietveld method
• 8 Symmetry mode refinements
• 9 Magnetic refinements
• 10 Stacking disorder
• 11 Total scattering methods
• 12 Multiple data sets
• 13 Appendix: Mathematical basics
• Index